If (ui + ei) is a LD set, the exercise is to prove the inequality:
sum{|ui|^2} >=1

I am trying to suppose, by contradiction, that the sum is less than 1, and then get that the vectors (ui+ei) are LI. I know this exercise is introductory to Linear Algebra, so it doesn't require deep theorems like "Frobenius norm" or matrices knowledge.